scholarly journals Approximation of random functions by stochastic Bernstein polynomials in capacity spaces

2021 ◽  
Vol 37 (2) ◽  
pp. 185-194
Author(s):  
SORIN G. GAL ◽  
CONSTANTIN P. NICULESCU
Keyword(s):  
Uniform Convergence ◽  
Quantitative Estimate ◽  
Random Function ◽  
Bernstein Polynomials ◽  
Random Functions ◽  
Quantitative Estimates ◽  
Univariate Case ◽  
Convergence In Capacity

Given a submodular capacity space, we firstly obtain a quantitative estimate for the uniform convergence in the Choquet p-mean, 1\le p<\infty, of the multivariate stochastic Bernstein polynomials associated to a random function. Also, quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

scholarly journals A Novel Construction of Constrained Verifiable Random Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Muhua Liu ◽  
Ping Zhang ◽  
Qingtao Wu
Keyword(s):  
Random Function ◽  
Secret Key ◽  
Bilinear Maps ◽  
Random Functions ◽  
Compute Function ◽  
Multilinear Maps ◽  
Verifiable Random Functions ◽  
Selective Security

Constrained verifiable random functions (VRFs) were introduced by Fuchsbauer. In a constrained VRF, one can drive a constrained key skS from the master secret key sk, where S is a subset of the domain. Using the constrained key skS, one can compute function values at points which are not in the set S. The security of constrained VRFs requires that the VRFs’ output should be indistinguishable from a random value in the range. They showed how to construct constrained VRFs for the bit-fixing class and the circuit constrained class based on multilinear maps. Their construction can only achieve selective security where an attacker must declare which point he will attack at the beginning of experiment. In this work, we propose a novel construction for constrained verifiable random function from bilinear maps and prove that it satisfies a new security definition which is stronger than the selective security. We call it semiadaptive security where the attacker is allowed to make the evaluation queries before it outputs the challenge point. It can immediately get that if a scheme satisfied semiadaptive security, and it must satisfy selective security.

scholarly journals Statically Aggregate Verifiable Random Functions and Application to E-Lottery

Cryptography ◽  
2020 ◽  
Vol 4 (4) ◽  
pp. 37
Author(s):  
Bei Liang ◽  
Gustavo Banegas ◽  
Aikaterini Mitrokotsa
Keyword(s):  
Random Function ◽  
Random Functions ◽  
Large Sets ◽  
Diffie Hellman ◽  
Winning Number ◽  
Verifiable Random Functions

Cohen, Goldwasser, and Vaikuntanathan (TCC’15) introduced the concept of aggregate pseudo-random functions (PRFs), which allow efficiently computing the aggregate of PRF values over exponential-sized sets. In this paper, we explore the aggregation augmentation on verifiable random function (VRFs), introduced by Micali, Rabin and Vadhan (FOCS’99), as well as its application to e-lottery schemes. We introduce the notion of static aggregate verifiable random functions (Agg-VRFs), which perform aggregation for VRFs in a static setting. Our contributions can be summarized as follows: (1) we define static aggregate VRFs, which allow the efficient aggregation of VRF values and the corresponding proofs over super-polynomially large sets; (2) we present a static Agg-VRF construction over bit-fixing sets with respect to product aggregation based on the q-decisional Diffie–Hellman exponent assumption; (3) we test the performance of our static Agg-VRFs instantiation in comparison to a standard (non-aggregate) VRF in terms of costing time for the aggregation and verification processes, which shows that Agg-VRFs lower considerably the timing of verification of big sets; and (4) by employing Agg-VRFs, we propose an improved e-lottery scheme based on the framework of Chow et al.’s VRF-based e-lottery proposal (ICCSA’05). We evaluate the performance of Chow et al.’s e-lottery scheme and our improved scheme, and the latter shows a significant improvement in the efficiency of generating the winning number and the player verification.

Survey of breast cancer patients concerning their knowledge and expectations of adjuvant therapy.

1998 ◽  
Vol 16 (2) ◽  
pp. 515-521 ◽  
Author(s):  
P M Ravdin ◽  
I A Siminoff ◽  
J A Harvey
Keyword(s):  
Breast Cancer ◽  
Adjuvant Therapy ◽  
Quantitative Estimate ◽  
Breast Cancer Survivors ◽  
Treatment Guidelines ◽  
Recurrence Risk ◽  
The United States ◽  
Breast Cancer Patients ◽  
Net Benefit ◽  
Quantitative Estimates

PURPOSE A survey of breast cancer survivors in the United States was conducted to define what they had been told about their prognosis and the value of adjuvant therapy, what they estimated their prognosis to be with and without adjuvant therapy, and what level of improvement they would have found minimally worthwhile. MATERIALS AND METHODS Survey questionnaires were mailed to individual members and member organizations of the National Alliance of Breast Cancer Organizations (NABCO). Questionnaires were returned anonymously in prepaid mailers. Five hundred sixty-two women responded. Of these, the 318 women who received adjuvant chemotherapy were included in this analysis. RESULTS Only 39% of the women recalled receiving quantitative estimates of their prognosis, and only 31% of women received a quantitative estimate both with and without adjuvant therapy. Sixty-eight percent of the women were able to provide a quantitative estimate for their outcome at 5 years both with and without adjuvant therapy. From these estimates, we calculated that the median estimated proportional risk reduction for recurrence that women thought they had achieved was 79%. Women were asked what degree of absolute benefit they would have found acceptable. The median acceptable extension of life expectancy was 3 to 6 months, and acceptable reduction in recurrence risk was 0.5% to 1.0%. However, there was considerable variation, with 27% of women not accepting less than 1 year and 26% not accepting a less than 5% reduction in recurrence risk. CONCLUSION In general, American women in the surveyed population (1) do not recall being provided quantitative estimates of outcome during the process of making decisions about adjuvant therapy, (2) overestimate the value of their therapy, and (3) often will accept remarkably low degrees of net benefit. Overall, these observations can be used to support the argument that improvements in doctor/patient communication may be important to truly informed decision-making, and that flexibility for individual patients' preferences should not be superseded by rigid treatment guidelines.

Fonctions Certaines Admettant des Répartitions Asymptotiques et Fonctions Aléatoires Stationnaires

1975 ◽  
Vol 12 (S1) ◽  
pp. 177-185
Author(s):  
A. Blanc-Lapierre
Keyword(s):  
Harmonic Analysis ◽  
Random Function ◽  
Random Variables ◽  
Random Variable ◽  
Type A ◽  
Asymptotic Distributions ◽  
Random Functions ◽  
Stationary Random Function ◽  
Translation Parameter ◽  
Character Independence

In the article below, we consider sets of non-random functions of time t admitting certain asymptotic distributions. Purely temporal and deterministic considerations lead us to associate to a set , say, of functions H(t) of this type, a space Ω of samples ω.To each function H(t) ⊂ , there corresponds a random variable h (ω). To the set of translated functions H(t + λ) of a function H(t) ⊂ , there corresponds a stationary random function of the translation parameter λ, say, h(λ, ω). We study the transposition to the set of non-random functions H(t) of such properties as moments, gaussian character, independence, harmonic analysis, and others, of the random variables h (ω) and of the random functions h (λ, ω).Some remarks are made concerning the links between ergodicity and the above problems.

Voronovskaja’s theorem, shape preserving properties and iterations for complex q-Bernstein polynomials

2011 ◽  
Vol 48 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Sorin Gal
Keyword(s):  
Convergence Theorem ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Bernstein Polynomials ◽  
Exact Order ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Voronovskaja’S Theorem ◽  
Shape Preserving Properties ◽  
Compact Disks

In this paper, first we prove Voronovskaja’s convergence theorem for complex q-Bernstein polynomials, 0 < q < 1, attached to analytic functions in compact disks in ℂ centered at origin, with quantitative estimate of this convergence. As an application, we obtain the exact order in approximation of analytic functions by the complex q-Bernstein polynomials on compact disks. Finally, we study the approximation properties of their iterates for any q > 0 and we prove that the complex qn-Bernstein polynomials with 0 < qn < 1 and qn → 1, preserve in the unit disk (beginning with an index) the starlikeness, convexity and spiral-likeness.

scholarly journals A Stone-Weierstrass theorem for random functions

1970 ◽  
Vol 2 (2) ◽  
pp. 233-236 ◽  
Author(s):  
A. Mukherjea
Keyword(s):  
Random Function ◽  
Random Variables ◽  
Compact Set ◽  
Mean Square ◽  
Weierstrass Theorem ◽  
Random Functions ◽  
The Given ◽  
Uniformly Bounded

It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.

VECTOR RANDOM FIELDS WITH LONG-RANGE DEPENDENCE

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 249-258 ◽  
Author(s):  
CHUNSHENG MA
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Random Function ◽  
Short Range ◽  
Diagonal Entry ◽  
Random Functions ◽  
Cross Covariance ◽  
Direct Covariance ◽  
Crucial Ingredient ◽  
Special Case

It is well-known that the crucial ingredient for a vector Gaussian random function is its covariance matrix, where a diagonal entry termed a direct covariance is simply the covariance function of a component but it seems no simple interpretation for an off-diagonal entry termed a cross covariance, which often make it hard to specify. In this paper we employ three approaches to derive vector random functions in space and/or time, which are not homogeneous (stationary) in general but contain the stationary case as a special case, and have long-range or short-range dependence.

scholarly journals On approximation properties of Baskakov-Schurer-Szász operators preserving exponential functions

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5433-5440 ◽  
Author(s):  
Övgü Yılmaz ◽  
Murat Bodur ◽  
Ali Aral
Keyword(s):  
Uniform Convergence ◽  
Generating Function ◽  
General Class ◽  
Quantitative Estimate ◽  
Moment Generating Function ◽  
Convergence Result ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Szász Operators

The goal of this paper is to construct a general class of operators which has known Baskakov-Schurer-Sz?sz that preserving constant and e2ax, a > 0 functions. Also, we demonstrate the fact that for these operators, moments can be obtained using the concept of moment generating function. Furthermore, we investigate a uniform convergence result and a quantitative estimate in consideration of given operator, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Schurer-Sz?sz operators and the recent sequence, too.

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